'Built in' position eased animation expression requesting thisComp.width

Try this:

mov = 10; // percent of comp width
lyrW = sourceRectAtTime().width;
movFrms = 24; // number of frames for the move
t = time - inPoint;
tMin = 0;
tMax = tMin + mov * thisComp.frameDuration;
value1 = 0 - lyrW;
value2 = thisComp.width * mov * .01;
x = ease(t, tMin, tMax, value1, value2);
y = value[1];
[x, y]

If the text layer is Left Justified, it will move from the left edge of the frame until the left edge is at 10% of the comp frame width in 24 frames.  The move starts with the layer in-point, which is more efficient than using a layer marker because Animation Presets cannot add layer markers.

You can add an Expression Control Slider for the movFrms count in the first line of the expression. You can also add a slider to the mov variable to control the ending x position.

If you really wanted to fiddle with adding markers, you could change the "tMax" variable to read the in point of the layer plus the marker time, but I think adding a slider for move time is more efficient.

If you want the move to work with different paragraph justifications, modify the starting and ending position by using sourceRectAtTime().left. This is how that looks:

mov = 24; // move timing in frames
movD = 10; // end position in % of comp width
L = sourceRectAtTime();
LLeft = L.left;
LWidth = L.width;
t = time - inPoint;
tMin = 0;
tMax = tMin + mov * thisComp.frameDuration;
value1 = 0 - LWidth - LLeft;
value2 = thisComp.width * movD * .01;
x = ease(t, tMin, tMax, value1, value2 - LLeft);
y = value[1];
[x, y]

You had an idea that I turned into another one of my Animation Presets.